A Functional Functional Interpretation

Pierre-Marie Pédrot 1, 2, *
* Corresponding author
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : In this paper, we present a modern reformulation of the Dialectica interpretation based on the linearized version of de Paiva. Contrarily to Gödel's original translation which translated HA into system T, our presentation applies on untyped λ-terms and features nicer proof-theoretical properties. In the Curry-Howard perspective, we show that the computational behaviour of this translation can be accurately described by the explicit stack manipulation of the Krivine abstract machine, thus giving it a direct-style operational explanation. Finally, we give direct evidence that supports the fact our presentation is quite relevant, by showing that we can apply it to the dependently-typed calculus of constructions with universes CCω almost without any adaptation. This answers the question of the validity of Dialectica-like constructions in a dependent setting.
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Pierre-Marie Pédrot. A Functional Functional Interpretation. CSL-LICS 2014 - Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2014, Vienna, Austria. ⟨10.1145/2603088.2603094⟩. ⟨hal-01111802⟩

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